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Gradient Flow Dynamics of Diagonal Linear Networks Analyzed

By PulseAugur Editorial · [3 sources] ·

Researchers have analyzed the gradient flow dynamics and implicit bias of diagonal linear networks for regression tasks under infinitesimal initialization. Their work extends previous theorems to deep and two-layer diagonal linear networks, demonstrating that training trajectories can be characterized by a specific algorithm. This algorithm converges to a modified L1 norm minimization problem, indicating that the implicit bias of these architectures corresponds to this modified norm in the infinitesimal initialization regime. The study also identifies the Structural Invariant Manifold as a key geometric structure influencing the learning process. AI

IMPACT Provides theoretical insights into the training dynamics and implicit bias of linear neural networks, potentially informing future model design.

RANK_REASON The cluster contains an academic paper detailing theoretical research on machine learning models.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

Gradient Flow Dynamics of Diagonal Linear Networks Analyzed

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COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · Jiajie Zhao, Jianxing Wang, Junjie Yang, Zhiwei Bai, Yaoyu Zhang ·

    Gradient Flow Dynamics and Implicit Bias of Diagonal Linear Networks under Infinitesimal Initialization

    arXiv:2607.12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear net…

  2. arXiv cs.LG TIER_1 English(EN) · Yaoyu Zhang ·

    Gradient Flow Dynamics and Implicit Bias of Diagonal Linear Networks under Infinitesimal Initialization

    We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal …

  3. Hugging Face Daily Papers TIER_1 English(EN) ·

    Gradient Flow Dynamics and Implicit Bias of Diagonal Linear Networks under Infinitesimal Initialization

    We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal …

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